Peaks digital

Figure 1. A comparison of the band shape obtained with a conventional "micro" TCD and a systematically designed small volume cell. Note the improvement both in width and the reduction in "tailing". (Methane peak, digitized data) Reproduced, with permission, from Ref. 1. Copyright 1977, Journal of Chromatographic Science,...

The simplest use of an NMR spectnim, as with many other branches of spectroscopy, is for quantitative analysis. Furthennore, in NMR all nuclei of a given type have the same transition probability, so that their resonances may be readily compared. The area underneath each isolated peak in an NMR spectnim is proportional to the number of nuclei giving rise to that peak alone. It may be measured to 1% accuracy by digital integration of the NMR spectnim, followed by comparison with the area of a peak from an added standard. 

Wlien is very short, which is almost always true with nuclei having/> 1/2, the dipolar contribution to relaxation will be negligible and, hence, there will be no contributions to the integral from either NOE or saturation. However, resonances more than about 1 kHz wide may lose intensify simply because part of the FID will be lost before it can be digitized, and resonances more than 10 kHz wide may be lost altogether. It is also hard to correct for minor baseline distortions when the peaks themselves are very broad. 

Even this number of signifieant digits is open to debate. Do we really know X to an aeeuiaey of 1 nm Does it matter for the relatively flat peaks in Eig. 2-3 What about d2M = 0.048 Is it better to report the eoneentration veetor to two signifieant digits Diseuss these questions in your report. 

A mass spectrum consists of a series of peaks at different m/z values, with the height of the peak proportional to the number of ions. A partial mass spectrum is shown in Figure 44.3 and is seen to be an analog signal that varies as the peaks rise from and fall to the baseline. Between the peaks are relatively long intervals when there is only the baseline. As described above, the signal is first digitized. 

If digital voltage readings (V1-V9) are taken at time intervals (At = 0.0001 sec in the example of Figure 44.4), then the area of the true peak (dotted) can be (mathematically) closely approximated to give ion abundance and, similarly, the time (tj to the center of gravity (centroid) of the peak can be determined, thereby giving the m/z value. 

Most mass spectrometers for analytical work have access to a large library of mass spectra of known compounds. These libraries are in a form that can be read immediately by a computer viz., the data corresponding to each spectrum have been compressed into digital form and stored permanently in memory. Each spectrum is stored as a list of m/z values for all peaks that are at least 5% of the height of the largest peak. To speed the search process, a much shorter version of the spectrum is normally examined (e.g., only one peak in every fourteen mass units). 

When a mass spectrum has been acquired by the spectrometer/computer system, it is already in digital form as m/z values versus peak heights (ion abundances), and it is a simple matter for the computer to compare each spectrum in the library with that of the unknown until it finds a match. The shortened search is carried out first, and the computer reports the best fits or matches between the unknown and spectra in the library. A search of even 60,000 to 70,000 spectra takes only a few seconds, particularly if transputers are used, thus saving the operator a great deal of time. Even a partial match can be valuable because, although the required structure may not have been found in the library, it is more than likely that some of the library compounds will have stractural pieces that can be recognized from a partial fit and so provide information on at least part of the structure of the unknown. 

This reduction in information is achieved by a preprocessor, which uses the digital voltages corresponding to an ion peak to estimate the peak area (ion abundance) and centroid (mean arrival time of peak, equivalent to m/z value) these two pieces of information — plus a flag to identify the peak — are stored. 

A computer file of about 19,000 peak wavenumbers and intensities, along with search software, is distributed by the Infrared Data Committee of Japan (IRDC). Donated spectra, which are evaluated by the Coblentz Society in coUaboration with the Joint Committee on Atomic and Molecular Physical Data (JCAMP), are digitized and made avaUable (64). Almost 25,000 ir spectra are avaUable on the SDBS system developed by the NCLl as described. A project was initiated at the University of California, Riverside, in 1986 for the constmction of a database of digitized ftir spectra. The team involved also developed algorithms for spectra evaluation (75). Other sources of spectral Hbraries include Sprouse Scientific, Aston Scientific, and the American Society for Testing and Materials (ASTM). 

A practical solution is to digitize the drawings and place them on CD s available to the maintenance and operation department. A good digital file reduces search time and helps the departments do a better job of keeping the machinery operating at their peak efficiency with minimal downtime. 

The sum expressed by equation (21) lends itself to a digital calculation and can be employed in an appropriate computer program to calculate actual peak profiles. In doing so, however, as (v) is measured in plate volumes and sample volumes are usually given in milliliters, they must be converted to plate volumes to be used with equation (21). To demonstrate the effect of a finite charge and the use of equation (21), the peak profiles resulting from a sample dispersed over the twenty-one consecutive plates of a column are shown in Figure 16. 

The sum expressed by equation (25) also lends itself to a digital solution and can be employed in an appropriate computer program to calculate actual peak profiles for different volumes of pure mobile phase that have been injected onto an equilibrated column. The values of (Xg) were calculated for a column having 500 theoretical plates and for sample volumes of 20, 50, 100 and 200 plate volumes, respectively. The curves relating solute concentration (Xe) to plate volumes of mobile phase passed through the column are shown in Figure 17. 

Apparatus. A gas chromatograph equipped with a flame-ionisation detector and data-handling system. The use of a digital integrator is particularly convenient for quantitative determinations, but other methods of measuring peak area may be used (Section 9.4). 

Computer Techniques McLafferty (Ref 63) has pointed out that the usefulness of elemental composition information increases exponentially with increasing mass, since the number of elemental combinations with the same integral mass becomes larger. There are compilations of exact masses and elemental compositions available (Refs 12a, 13 18a). Spectral interpretation will be simplified in important ways if elemental compositions of all but, the smallest peaks are determined. Deriving the elemental compositions of several peaks in a spectrum is extremely laborious and time-consuming. However, with the availability of digital computers such tasks are readily performed. A modern data acquisition and reduction system with a dedicated online computer can determine peak centroids and areas for all peaks, locate reference peaks, interpolate between them to determine the exact masses of the unknown peaks, and find within minutes elemental compositions of all ions in a spectrum (Refs 28b 28c)... 

Figure 3.12 Comparison of the chromatographic peak shapes obtained from (a) analogue and (b,c) digital detectors, and the effect on peak shape of the number of data points defining the signal.

Jones, R., High-Pass and Band-Pass Digital Filtering with Peak to Trough Measurement Applied to Quantitative Ultraviolet Spectrometry, Analyst 112, November 1987, 1495-1498. 

Figure 1.29 shows the effect of digital resolution on the appearance of signals. It is important to remember that each data point in the FID contains information about every peak in the spectrum, so as more data p>oints are accumulated, and the FIDs acquired for a longer period, a finer digital resolution is achieved. 

The number of data points to be chosen in the Fj and F2 domains is dictated not only by the desired resolution but by other, external considerations, such as the available storage space in the computer, and the time that can be allocated for data acquisition, transformation, and other instrument operations. Clearly, to avoid any unnecessary waste of time, we should choose the minimum resolution that would yield the desired information. Thus, if the peaks are separated by at least 1 Hz, then the desired digital resolution should be R/2 = V2 Hz to allow for signal separation in the F domain. The resolution considerations in the F and F domains may be different, depending on what information is required from each domain... 

Figure 5.28 A schematic drawing of an AMX spin system representing coupling interactions recorded at low digital resolution so that no fine splittings are visible. Note the symmetrical appearance of the cross-peaks on either side of the diagonal.

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